Linker histone H1 (H1) is an abundant chromatin-binding protein that acts as an epigenetic regulator binding to nucleosomes and altering chromatin structures and dynamics. Nonetheless, the mechanistic details of its function remain poorly understood. Recent work suggest that the number and position of charged side chains on the globular domain (GD) of H1 influence chromatin structure and hence gene repression. Here, we solved the solution structure of the unbound GD of human H1.0, revealing that the structure is almost completely unperturbed by complex formation, except for a loop connecting two antiparallel beta-strands. We further quantified the role of the many positive charges of the GD for its structure and conformational stability through the analysis of 11 charge variants. We find that modulating the number of charges has little effect on the structure, but the stability is affected, resulting in a difference in melting temperature of 26 K between GD of net charge +5 versus +13. This result suggests that the large number of positive charges on H1-GDs have evolved for function rather than structure and high stability. The stabilization of the GD upon binding to DNA can thus be expected to have a pronounced electrostatic component, a contribution that is amenable to modulation by posttranslational modifications, especially acetylation and phosphorylation.